Undergraduate course in Probability and statistical inference
In particular, basic knowledge of the following topics is required:
- Main probability distributions
- Estimation and confidence intervals
- Hypothesis testing
In this course, the student will develop statistical tools to monitor and understand innovation processes: they will learn how to compute trends and forecasts, quantify uncertainty and assess the impact of changes in the era of innovation and global warming mitigation.
Working in an advanced computing environment (Matlab, R or Python), the student will learn to provide an appropriate graphical representation of data and build statistical models for descriptive, interpretative, predictive and simulation purposes.
They will develop significant operational experience through participation in a working group for the development of a statistical project.
In particular, the student will work with methods of time series analysis and statistical forecasting useful for describing time dynamics, predicting future short-term behaviour, and performing scenario and simulation analyses. Particular attention will be given to uncertainty assessment.
Review of statistical inference.
Data over time and time series. Graphical representation of time series.
Multivariate data and the variance-covariance matrix.
The multivariate normal distribution. Testing normality.
The classical regression model: assumptions, estimation and static forecast. Selection of variables, predictive performance, cross-validation.
Nonparametric, spline and neural networks regression models.
Data over time and the autocorrelation function.
Auto-regressive and moving average models.
Stationarity and invertibility. Parameter estimation and model selection.
Model diagnostic and validation.
Dynamic forecasting: one-step and multi-step forecasts, predictive performance.
Time series regression models.
Intervention analysis and change detection.
State-space models: state equations, measurement equations, filtering, prediction and smoothing.
The above topics will be linked to one or more data sets that will be used a) by the teacher to illustrate the methods and b) by the student who will learn to work on them through Matlab, R or Python.
Lectures and discussions (70%)
Case studies (30%)
Participation in a working group for the development of a statistical project.
- Project presentation and discussion in front of the class (50%)
- Individual oral examination on methods used to develop the project (50%)